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I want a function or operation that satisfy below conditions:
with given $x,y$ anyone can compute $z$;
but with given $x$ or $y$ solely, no anyone can compute $z$;
and with given $z$ anyone can compute or derive $x$ and $y$.

Note: $x,y$ and $z$ are variable (integer, float, string or anything).

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The conditions are equivalent to asking for a bijective function from $A\times A$ to $B$, for appropriate $A$ and $B$. Note that the OP doesn't necessarily want an operation. –  Git Gud Jan 17 at 9:28
For strings $x,y$ that don't contain $\#$, you can use $(x,y)\mapsto x\#y=z$. –  Listing Jan 17 at 9:33
If $x,y,z$ are supposed to range over one and the same set, I believe the kind of structure you're asking about is called a Jónsson-Tarski algebra. –  bof Jan 17 at 9:39
@Listing: Note. Three variables x,y and z must be in same length. –  user34221 Jan 17 at 9:39
I think chinese remainders theorem in cyclic groups works fine. –  mak Jan 17 at 9:42

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